The vector v lies in the subspace of R^3 and is spanned by the set B = {u1, u2}. Making use of the fact that the set B is orthogonal, express v in terms of B where, v = 1 -2 -13 B = 1 1 2 , 1 3 -1 v is a matrix and B is a set of 2 …

Mark each of the following True or False. ___ a. All vectors in an orthogonal basis have length 1. ___ b. A square matrix is orthogonal if its column vectors are orthogonal. ___ c. If A^T is orthogonal, then A is orthogonal. ___ d. …

I have 3 points: P(-3, 1, 2), Q(-1, 2, 3), R(2, 1, 0) and I need to find a nonzero vector orthogonal to the plane through these three points. I seem to recall this having something to do with the cross product, so I mad vectors PQ …

Ok this is the last one I promise! It's from a sample exam and I'm practicing for my finals :) Verify if the following 4 points are consecutive vertices of a parallelogram: A(1,-1,1); B(3,0,2);C(2,3,4);D(0,2,3) (b) Find an orthogonal …

I'm doing a bunch of practice finals and I don't know how to approach this problem. Find a vector a such that a is orthogonal to < 1, 5, 2 > and has length equal to 6. If I want to find a vector that is orthogonal to <1,5,2>, …